Model for reversible nanoparticle assembly in a polymer matrix

Abstract

The clustering of nanoparticles ͑NPs͒ in solutions and polymer melts depends sensitively on the strength and directionality of the NP interactions involved, as well as the molecular geometry and interactions of the dispersing fluids. Since clustering can strongly influence the properties of polymer-NP materials, we aim to better elucidate the mechanism of reversible self-assembly of highly symmetric NPs into clusters under equilibrium conditions. Our results are based on molecular dynamics simulations of icosahedral NP with a long-ranged interaction intended to mimic the polymer-mediated interactions of a polymer-melt matrix. To distinguish effects of polymer-mediated interactions from bare NP interactions, we compare the NP assembly in our coarse-grained model to the case where the NP interactions are purely short ranged. For the "control" case of NPs with short-ranged interactions and no polymer matrix, we find that the particles exhibit ordinary phase separation. By incorporating physically plausible long-ranged interactions, we suppress phase separation and qualitatively reproduce the thermally reversible cluster formation found previously in computations for NPs with short-ranged interactions in an explicit polymer-melt matrix. We further characterize the assembly process by evaluating the cluster properties and the location of the self-assembly transition. Our findings are consistent with a theoretical model for equilibrium clustering when the particle association is subject to a constraint. In particular, the density dependence of the average cluster mass exhibits a linear concentration dependence, in contrast to the square root dependence found in freely associating systems. The coarse-grained model we use to simulate NP in a polymer matrix shares many features of potentials used to model colloidal systems. The model should be practically valuable for exploring factors that control the dispersion of NP in polymer matrices where explicit simulation of the polymer matrix is too time consuming.

Anisotropic aggregation in a simple model of isotropically polymer-coated nanoparticles

“…For low values of the functionality f and polymer size q = 2r g /σ , a grand-canonical approach will result in a bulk solid of NPs. However, the presence of the polymer matrix was shown to provide stabilization to a cluster phase for isotropic particles in the absence of highly directional interactions [16,17]. The origin of this equilibrium cluster formation was found to be a weak, long-ranged repulsion caused by chain connectivity in the polymer matrix.…”

String model for the dynamics of glass-forming liquids

“…(11) because of the approximation A ≈ r. Equations (10) and (11) imply that L saturates to a constant value at low T, a point extensively discussed below. In living polymer solutions, the magnitude of r (and thus A by analogy) links the string mass at high and low T and also governs the cooperativity of the polymerization transition, 69 as measured by the rate of change of L(T), and the magnitude of the change in the specific heat; similar definitions of cooperativity have been applied to GF liquids. 19,70 In the living polymerization model, the order parameter is the extent of polymerization, defined by the fraction of monomers forming polymeric structures.…”

Nanoparticle-regulated phase behavior of ordered block copolymers

“…In this spirit, we note that independent studies have shown that the stability of block copolymer nanostructures can likewise be enhanced through the incorporation of selective 37 or functional 38 homopolymers that remain mixed within (and do not macrophase-separate from) the copolymer nanostructure. Addition of selective nanoparticles to ordered block copolymers may therefore not only yield novel, spatially-modulated hybrid materials via nanoparticle assembly 39 for a wide variety of growing nanotechnologies, but also provide an alternative physical means by which to promote polymeric nanostructure development. …”